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Loafers

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But now I'd like to know how would you find the ratio of a triangle with an messy angle such as 37 or 98? Most teachers would tell me to punch it in the calculator... but I'd like to have a better understanding than just what my calculator tells me... So I guess what I should be asking is, what does a calculator do to solve the sin/cos/tan of 37,94, 261, etc..? How does it determine what the measurements of a triangle are to get the ratio? I wish to understand trig functions better than just soh/cah/toa and guesstimate.

I only know a little bit of calculus so a simple explanation, if possible, would greatly be appreciated.